![SOLVED:Suppose (u, uT Bv defines an inner product in R" for some n X n matrix B Explain why B must be invertible. marks) Explain why B must be positive definite. marks) SOLVED:Suppose (u, uT Bv defines an inner product in R" for some n X n matrix B Explain why B must be invertible. marks) Explain why B must be positive definite. marks)](https://cdn.numerade.com/ask_images/b2158fa3363a40e681883e24c97f64ad.jpg)
SOLVED:Suppose (u, uT Bv defines an inner product in R" for some n X n matrix B Explain why B must be invertible. marks) Explain why B must be positive definite. marks)
![SOLVED:Show that if B is m xn; then B"B is positive semidefinite; and if B is n xn and invertible, then BTB is positive definite. First suppose only that B is mxn: SOLVED:Show that if B is m xn; then B"B is positive semidefinite; and if B is n xn and invertible, then BTB is positive definite. First suppose only that B is mxn:](https://cdn.numerade.com/ask_images/d54a131511c743cfbfbb40c095934ef0.jpg)
SOLVED:Show that if B is m xn; then B"B is positive semidefinite; and if B is n xn and invertible, then BTB is positive definite. First suppose only that B is mxn:
![SOLVED:12. Let A= [41 4] Ax = 112 21172 +amz (21 T2)2 + (a _ 1)zz Write and decide for what values of a is A positive definite Do the same to SOLVED:12. Let A= [41 4] Ax = 112 21172 +amz (21 T2)2 + (a _ 1)zz Write and decide for what values of a is A positive definite Do the same to](https://cdn.numerade.com/ask_images/a11a0c2e0c8a424b8d5fb8643ba3a7d4.jpg)
SOLVED:12. Let A= [41 4] Ax = 112 21172 +amz (21 T2)2 + (a _ 1)zz Write and decide for what values of a is A positive definite Do the same to
![SOLVED:Mxxe L (R): the set of m X n real matrices_ A € Mnxn (R) is positive definite if A = AT and xT Ax > 0 for all z = 0 SOLVED:Mxxe L (R): the set of m X n real matrices_ A € Mnxn (R) is positive definite if A = AT and xT Ax > 0 for all z = 0](https://cdn.numerade.com/ask_images/e75443ab5223437bba7ae748c8352ea1.jpg)
SOLVED:Mxxe L (R): the set of m X n real matrices_ A € Mnxn (R) is positive definite if A = AT and xT Ax > 0 for all z = 0
![Showing that A-transpose x A is invertible | Matrix transformations | Linear Algebra | Khan Academy - YouTube Showing that A-transpose x A is invertible | Matrix transformations | Linear Algebra | Khan Academy - YouTube](https://i.ytimg.com/vi/ESSMQH6Y5OA/maxresdefault.jpg)